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upwlev2

Single-level reconstruction of 2-D wavelet decomposition

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    Syntax

    [nc,ns,ca] = upwlev2(c,s,wname)
    [nc,ns,ca] = upwlev2(c,s,LoR,HiR)

    Description

    [nc,ns,ca] = upwlev2(c,s,wname) performs the single-level reconstruction of the wavelet decomposition structure [c,s] using the wavelet specified by wname, giving the new structure [nc,ns], and extracts the last approximation coefficients matrix ca.

    [nc,ns,ca] = upwlev2(c,s,LoR,HiR) performs the single-level reconstruction using the specified lowpass and highpass wavelet reconstruction filters LoR and HiR, respectively.

    example

    Examples

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    Open Live Script

    Load an image.

    load porche
image(X)
colormap(map)

    Figure contains an axes object. The axes object contains an object of type image.

    Save the current extension mode, and set the extension mode to zero-padding.

    origmode = dwtmode("status","nodisp");
dwtmode("zpd","nodisp")

    Obtain the DWT decomposition of the image down to level 2. Use the Haar wavelet.

    wv = "haar";
[c,s] = wavedec2(X,2,wv);
size(c)
    ans = 1×2

           1      262144


    s
    s = 4×2

   128   128
   128   128
   256   256
   512   512

    Use the appcoef2 function to extract the approximation coefficients from the wavelet decomposition structure [c,s].

    a = appcoef2(c,s,wv);
size(a)
    ans = 1×2

   128   128

    Perform the single-level reconstruction of the wavelet decomposition structure [c,s]. Also obtain the approximation matrix at level 2. Confirm the total number of coefficients has not changed, and the approximation coefficients obtained using appcoef2 and upwlev2 are equal.

    [nc,ns,ca] = upwlev2(c,s,wv);
size(nc)
    ans = 1×2

           1      262144


    ns
    ns = 3×2

   256   256
   256   256
   512   512


    max(max(abs(a-ca)))
    ans = 
0

    Restore the original extension mode.

    dwtmode(origmode,"nodisp")

    Input Arguments

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    Wavelet decomposition vector, specified as a real-valued vector. The vector c contains the approximation and detail coefficients organized by level. The bookkeeping matrix s is used to parse c. c and s are outputs of wavedec2.

    Data Types: double

    Bookkeeping matrix, specified as an integer-valued matrix. The matrix s contains the dimensions of the wavelet coefficients by level and is used to parse the wavelet decomposition vector c. c and s are outputs of wavedec2.

    Data Types: double

    Analyzing wavelet, specified as a character vector or string scalar. wname must specify the same wavelet used to obtain the original wavelet decomposition structure [c,s]. The wavedec2 function supports only orthogonal and biorthogonal wavelets. See wfilters for a list of orthogonal and biorthogonal wavelets.

    Data Types: char | string

    Wavelet reconstruction filters, specified as a pair of even-length real-valued vectors. LoR is the lowpass reconstruction filter, and HiR is the highpass reconstruction filter. LoR and HiR must correspond to the wavelet used to obtain the original wavelet decomposition structure [c,s]. The lengths of LoR and HiR must be equal. See wfilters for a list of orthogonal and biorthogonal wavelets.

    Data Types: double

    Output Arguments

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    Wavelet decomposition, returned as a vector. The vector contains the wavelet coefficients. [c,s] is a decomposition at level n = size(s,1)-2, so [nc,ns] is the same decomposition at level n-1. The bookkeeping matrix ns contains the contains the dimensions of the wavelet coefficients by level and is used to parse the wavelet decomposition vector nc.

    Data Types: double

    Bookkeeping matrix, returned as a matrix of positive integers. The bookkeeping matrix is used to parse the coefficients in the wavelet decomposition nc by level.

    Data Types: double

    Approximation matrix at level n, where n = size(s,1)-2.

    If c and s are obtained from an indexed image analysis or a truecolor image analysis, ca is an m-by-n matrix or an m-by-n-by-3 array, respectively. For more information, see wavedec2.

    For more information on image formats, see image and imfinfo.

    Data Types: double

    Version History

    Introduced before R2006a

    See Also

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